• 한국수학사학회지
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• 제32권4호
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• pp.159-173
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• 2019

In this paper, we examine the brief history of the ring of four almonds regarding Mesopotamian mathematics, and present reasons why the Omar Khayyam's triangle, a special right triangle in a ring of four almonds, was essential for artisans due to its unique pattern. We presume that the ring of four almonds originated from a point symmetry figure given two concentric squares used in the proto-Sumerian Jemdet Nasr period (approximately 3000 B.C.) and a square halfway between two given concentric squares used during the time of the Old Akkadian period (2340-2200 B.C.) and the Old Babylonian age (2000-1600 B.C.). Artisans tried to create a new intricate pattern as almonds and 6-pointed stars by subdividing right triangles in the pattern of the popular altered Old Akkadian square band at the time. Therefore, artisans needed the Omar Khayyam's triangle, whose hypotenuse equals the sum of the short side and the perpendicular to the hypotenuse. We presume that artisans asked mathematicians how to construct the Omar Khayyam's triangle at a meeting between artisans and mathematicians in Isfahan. The construction of Omar Khayyam's triangle requires solving an irreducible cubic polynomial. Omar Khayyam was the first to classify equations of integer polynomials of degree up to three and then proceeded to solve all types of cubic equations by means of intersections of conic sections. Omar Khayyam's triangle gave practical meaning to the type of cubic equation $x^3+bx=cx^2+a$. The work of Omar Khayyam was completed by Descartes in the 17th century.

• 한국작물학회지
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• 제53권3호
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• pp.297-302
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• 2008

Application of genotype by environment ($G\;{\times}\;E$) interaction would be used for identifying optimum test condition of the varietal adaptation in the establishment of breeding purpose. Yield and yield components were used to perform additive main effect and multiplicative interaction (AMMI) analysis. Significant difference for $G\;{\times}\;E$ interaction were observed for all variable examined. For yield, 0.18 of total sum of squares corresponded to $G\;{\times}\;E$ interaction. Correlation analysis was carried out between genotypic scores of the first interaction principal component axis (IPCA 1) for agronomic characters. Significant correlations were observed between IPCA 1 for yield and capsule bearing stem length (CBSL), number of capsule per plant (NOC). The biplot of grain yield means for IPCA1 which accounted for 34% of the variation in total treatment sums of squares showed different reaction according to $G\;{\times}\;E$ interaction, genotypes and environments. Taegu showed relatively lower positive IPCA1 scores, and it also showed smaller coefficient variation of yield mean where it is recommendable as a optimal site for the sesame cultivar adaptation and evaluation trial. In case of variables, Yangbaek and M1 showed relatively lower IPCA1 scores, but the score direction showed opposite each other on the graph. Ansan, Miryang1, Miryang4, and Miryang6 seemed to be similar group in view of yield response against IPCA1 scores. These results will be helpful to select experimental site for sesame in Korea to minimize $G\;{\times}\;E$ interaction for the selection of promising genotype with higher stability.

• 응용통계연구
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• 제26권3호
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• pp.431-440
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• 2013

우리는 두꺼운 꼬리를 갖는 분포의 모수를 추정하는 방법론을 연구하였다. 일반적으로 MLE(최대우도 추정량)가 모수추정 방법론중에 가장 많이 사용되는데, 이는 MLE가 점근적 일치성과 정규성 그리고 효율성을 가지고 있기 때문이다. 하지만 MLE가 늘 가장 좋은 추정법은 아니다. 어떤 경우에는 MLE가 존재하지 않을 수도 있고 계산이 안정적이지 않을 수도 있다. 본 논문에서는 비선형 최소제곱추정법을 이용한 모수추정 방법론을 제시하고 그 성능을 MLE와 비교하였다. NLS 추정량은 empirical CDF와 이론적 CDF의 차이의 제곱을 최소화 하는 방법론이다. 본 논문에서는 두꺼운 꼬리를 가지는 다양한 분포하에서 우리가 제안하는 NLS방법론과 MLE와의 성능을 비교하였다. 그 결과, Burr 분포에서 표본의 수가 적을 때 우리의 방법론이 MLE보다 좋은 성능을 보여주었고, Frechet 분포에서도 좋은 결과를 얻을 수 있었다.

• 지적과 국토정보
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• 제45권2호
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• pp.117-130
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• 2015

도근점측량과 같은 수평위치를 결정하는 방법 중 최소제곱법은 확률이론에 근거하여 잔차의 분산이 최소가 되는 조건을 만족하는 최확값을 산출하는 방법이다. 본 논문에서는 도선법으로 계산되는 현행 지적도근점측량의 성과와 최소제곱법을 적용한 도근점의 계산성과를 비교하고, 네트워크-RTK 측량결과와 각각의 조정방법에 대한 평균오차를 확인하였다. 실험 결과 최소제곱법이 도선법에 비해 폐합오차를 각 측점에 균등하게 배분하는 것을 확인하였으며, 네트워크-RTK 성과와의 평균오차도 도선법은 2.7cm, 최소제곱법은 2.2cm 산출되었다. 또한 과대오차가 발생한 경우 이를 확인하기 위한 방법으로 정방향 초기값과 역방향 초기값을 이용하여 수평각 과대오차를 확인할 수 있었으며, 관측된 측선거리와 계산된 측선 거리의 차이를 이용하여 거리 과대오차가 발생한 측선을 예측할 수 있었다.

• Imaging Science in Dentistry
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• 제53권1호
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• pp.43-51
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• 2023

Purpose: This study aimed to assess texture analysis(TA) of cone-beam computed tomography (CBCT) images as a quantitative tool for the differential diagnosis of odontogenic and non-odontogenic maxillary sinusitis(OS and NOS, respectively). Materials and Methods: CBCT images of 40 patients diagnosed with OS (N=20) and NOS (N=20) were evaluated. The gray level co-occurrence (GLCM) matrix parameters, and gray level run length matrix texture (GLRLM) parameters were extracted using manually placed regions of interest on lesion images. Seven texture parameters were calculated using GLCM and 4 parameters using GLRLM. The Mann-Whitney test was used for comparisons between the groups, and the Levene test was performed to confirm the homogeneity of variance (α=5%). Results: The results showed statistically significant differences(P<0.05) between the OS and NOS patients regarding 3 TA parameters. NOS patients presented higher values for contrast, while OS patients presented higher values for correlation and inverse difference moment. Greater textural homogeneity was observed in the OS patients than in the NOS patients, with statistically significant differences in standard deviations between the groups for correlation, sum of squares, sum of entropy, and entropy. Conclusion: TA enabled quantitative differentiation between OS and NOS on CBCT images by using the parameters of contrast, correlation, and inverse difference moment.

• Asian-Australasian Journal of Animal Sciences
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• 제10권2호
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• pp.240-244
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• 1997

This study was conducted in North Sulawesi, Indonesia to identify the factors affecting reproductive efficiency and to determine the contribution of each factor in reproductive efficiency of Indonesian native cows. Records of reproductive efficiency, body size (hip height, body weight, body length, heart girth) as well as age on one hundred and sixty seven Indonesian native cows (seventy six cows of the Bali breed and ninety one cows of the synthetic breed from unknown proportion of th Madura, the Sumba and the Ongole breeds) of 58 farmers were available in this research. The data were analyzed by covariance analysis using SAS package including reproductive efficiency as a dependent variable and breed, body size (hip height, body weight, body length, heart girth) and age of cows as independent variables. The contribution of each independent factor to dependent variable was estimated as the percentage of the sum of square in the corrected total sum of squares. The results showed that body weight and body size of cows would be considered as th most important factors affecting reproductive efficiency of Indonesian native cows. Therefore, the reproductive efficiency could be increased by 1) using cows that reached a target weight of at least 250 kg, 2) using cows with relatively well developed height at hip of at least 117 cm, heart girth of at least 150 cm, and body length of at least 125 cm, 3) keeping breeding cows that reach a target age of 24 months old with the maximum interval between postpartum and next breeding season of 90 days for each year, and 4) using good nutritional feeding to reach the optimum weight and body condition.

• Imaging Science in Dentistry
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• 제53권2호
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• pp.109-115
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• 2023

Purpose: The aim of this study was to evaluate changes in the trabecular bone through texture analysis and compare the texture analysis characteristics of different areas in patients with medication-related osteonecrosis of the jaw (MRONJ). Materials and Methods: Cone-beam computed tomographic images of 16 patients diagnosed with MRONJ were used. In sagittal images, 3 regions were chosen: active osteonecrosis(AO); intermediate tissue (IT), which presented a zone of apparently healthy tissue adjacent to the AO area; and healthy bone tissue (HT) (control area). Texture analysis was performed evaluating 7 parameters: secondary angular momentum, contrast, correlation, sum of squares, inverse moment of difference, sum of entropies, and entropy. Data were analyzed using the Kruskal-Wallis test with a significance level of 5%. Results: Comparing the areas of AO, IT, and HT, significant differences (P<0.05) were observed. The IT and AO area images showed higher values for parameters such as contrast, entropy, and secondary angular momentum than the HT area, indicating greater disorder in these tissues. Conclusion: Through texture analysis, changes in the bone pattern could be observed in areas of osteonecrosis. The texture analysis demonstrated that areas visually identified and classified as IT still had necrotic tissue, thereby increasing the accuracy of delimiting the real extension of MRONJ.

• 오토저널
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• 제14권5호
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• pp.95-106
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• 1992

Active control of acoustic noise is an application area of adaptive digital signal processing with increasingly interest along the last year. This work studies the implementation of the multichannel LMS filter and the application of this algorithm for the reduction of the noise inside a vechicle cabin using a number of 'secondary sources' drived by adaptive filtering of a reference noise source. Firstly, we propose the use of an adaptive method for the time-varient optimal convergence factor. Secondly, we propose the use of adaptive delayed inverse model to estimate the elastic-acoustic transfer function presented in vechicle cabin. The original, primary source is often periodic, with a known fundamental frequency. A suitably filtered reference signal can thus be used to drive the secondary sources. An algorithm is presented for adapting the coefficients of an FIR filter feeding such a secondary source in such a way as to minimize the output of a suitably placed microphone. In this algorithm, the coefficients of adaptive filter driving an array of secondary sources can be adapted to minimize the sum of the squares of the outputs of a number of error microphones. The multichannel LMS algorithm displays that such an algorithm is considered suitable to used for the global suppression of noise in vehicle cabin.

• Horticulture, Environment, and Biotechnology : HEB
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• 제59권6호
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• pp.919-927
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• 2018

To compare the antioxidant properties and flavonols in various parts; dry skin (DS) and edible portion (EP), of 8 red onions (Allium cepa L, ROs), total content of phenolics (TPC), flavonoids (TFC), and anthocyanins (TAC) and DPPH radical scavenging properties were estimated and the content of six flavonols were quantified by HPLC-PDA analysis. The major component of DS and EP of RO was quercetin and quercetin-4'-glucoside, respectively. Score plots of the PCA and PLS-DA were segregated by flavonols content and antioxidant properties according to the EP and DS of ROs. Loading plot of the PCA showed that the quercetin and sum of flavonol content were highly correlated with antioxidant activity of ROs. Therefore, flavonol content and antioxidant activity can be used as markers for distinct parts of ROs.

• 국제강구조저널
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• 제18권5호
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• pp.1508-1524
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• 2018

Hysteretic energy dissipating devices (HEDDs) have been increasingly applied to building construction to improve the seismic performance. The seismic responses of such damped structures are significantly affected by HEDD's structural properties. An accurate investigation on the propagation of HEDD's structural properties is required for reasonable evaluation of the seismic performance of a structure. This study aims to develop simplified methods that can estimate the collective uncertainty-propagation to the seismic response of damped structures employing HEDDs. To achieve this, three- and six-story steel moment-resisting frames were selected and the propagations of the individual HEDD's property-uncertainties were evaluated when they are subjected to various levels of seismic demand. Based on the result of individual uncertainty-propagations, a simplified method is proposed to evaluate the variation of seismic response collectively propagated by HEDD's property-uncertainties and is verified by comparing with the exact collective uncertainty-propagation calculated using the Monte Carlo simulation method. The proposed method, called as a modified SRSS method in this study, is established from a conventional square root of the sum of the squares (SRSS) method with the relative contributions of the individual HEDD's property-uncertainty propagations. This study shows that the modified SRSS method provides a better estimation than the conventional SRSS method and can significantly reduce computational time with reasonable accuracy compared with the Monte Carlo simulation method.